hi! Relatively new here (I’m coming from setlist.fm) and kinda confused haha. So there’s this 2000s Chicago pop-punk band 15 Minutes Late who renamed themselves to Logan Square in 2006ish (as per the annotation on that artist profile). There’s a separate artist profile for them as Logan Square here - should there be a separate artist profile for renames, or should it be Logan Square with an alias set up for 15 Minutes Late (and check the box for ‘this alias is no longer current’)?
But, here’s where it gets more complicated. Logan Square is active again as of 2019 (idk when they broke up in the first place, but I’m guessing late 2006/2007?) as per their instagram…but now they’re going by 15 Minutes Late again. So they renamed to Logan Square in 2006 and then un-renamed in 2019…my best guess would be to keep the 15 Minutes Late profile and set it up with an alias of Logan Square from 2006-2019, but then the existing Logan Square artist profile would need to be merged into the 15 Minutes Late profile which i have NO idea how to do. help!
Welcome to MB!
It depends, if they’re different projects by the same people it makes sense to keep them both as separate artist entries in MB. If however it is just a name change then it would make sense to merge them and set up the aliases and add the time periods of when they had which alias.
Merging artists isn’t as difficult as you might think. Here’s the documentation you could read up on, and here’s a video explaining the process. Basically you look for the merge button on the right hand side of the artist page. After you’ve clicked it you go to other artist entry and also click the merge button there.
This will bring you to a new page. There you can select which one the other should be merged into. Also you can select a checkbox whether or not to change all the artists credits to the target’s name (the one you just selected). This is useful for instance when one of either artists contained a typo. In your case you wouldn’t want to use this checkbox though, because you want to keep the data of which albums was released under which name. Make sure to also add some source in the edit note so others can see that you are correct.
If something is merged incorrectly it can be a lot of work to undo it. So if you’re uncertain about it make sure to have some other people look at it for instance by discussing it on the forum before you put in the edit. Or by asking for some eyes on it after you’ve made the edit in the Request For Votes thread. It will take some time for the edit to finish, people first get a chance to vote on it. An alias is automatically created when artists are merged, but you will want to go back to it after the merge is completed and set it up properly with all the dates.
Good luck! 
It’s hard to tell from the bios I’ve looked at (AllMusic, Last.fm) whether the name changes were associated with personnel changes / breakups or not.
If you end up merging, please make sure that the 15 Minutes Late artist has a disambiguation comment like “aka Logan Square” to make it less likely that someone else will create another Logan Square artist again.
If the artists remain separate, you can add renamed into/from relationships to link them:
I just verified that it’s possible to create a second relationship in the opposite direction describing the rename back:
If going that route, it might be cleaner to just have a single renamed-into relationship with begin/end dates describing the period when they were going as Logan Square, though.